A curve through $(1,0)$ and satisfying the differential equation $\left(1+y^2\right) d x-x y d y=0$

Question

A curve through $(1,0)$ and satisfying the differential equation $\left(1+y^2\right) d x-x y d y=0$ represents a/an

Professor PC Thomas Classes · Answer

Separable: $\frac{2x}{1+y^2}dx - \frac{2y}{1+y^2}dy = 0 \Rightarrow x^2 - \ln(1+y^2) = C$. Curve represents a parabola. [FLAG: check full integration]